Answer to Question #372 in Statistics and Probability for Dong-Sun

Question

Student came to the exam knowing only 24 questions out of 30. If he doesn’t know the answer on a question he gets a second one. Student can pass the exam if he answers at least one question. What is the probability of passing the exam?

Answer 1

There are two ways the student can pass the exam:

1 – the first given question is one of 24 he knows. The probability to get it is: P(1) = 24/30 = 0.8;
2 – the first given question is one of 6 he doesn’t know, but the second one is one of 24 he knows (note that there are 29 questions left). The probability to get them is: P(2) = 6/30 * 24/29 ≈ 0.17.

As these events are independent, the probability to pass the exam is: P = P(1) + P(2) ≈ 0.8 + 0.17 ≈ 0.97.